Answer:
[PCl₃] = [Cl₂] = 0.035M
[PCl₅] = 0.059M
Explanation:
Based on the chemical reaction, Kc is:
Kc = 49 = [PCl₅] / [PCl₃] [Cl₂]
Where [] are the concentrations in equilibrium of each species
The initial concentration of the reactants is:
[PCl₃] = [Cl₂] = 0.75mol / 8.0L = 0.094M
The reactants must be consumed whereas PCl₅ will be produced. That is:
[PCl₃] = [Cl₂] = 0.094M - X
[PCl₅] = X
Where X is the reaction coordinate
Replacing in Kc expression:
49 = [X] / [0.094 - X] [0.094 - X]
49 = [X] / 0.008836 - 0.188 X + X²
0.432964 - 9.212 X + 49 X² = X
0.432964 - 10.212 X + 49 X² = 0
Solving for X
X = 0.059M → Right solution
X = 0.15M → False solution. Will produce negative concentrations
Replacing:
[PCl₃] = [Cl₂] = 0.094M - 0.059M = 0.035M
[PCl₅] = 0.059M
[PCl₃] = [Cl₂] = 0.035M
[PCl₅] = 0.059M
